1. Field of the Invention
The present invention relates to a method of electronically generating data representative of curved surfaces and the apparatus based upon the method, and more specifically to a method of freely generating data representative of a new curved surface by applying a local deformation on a source curved surface using computer graphic techniques and apparatus.
2. Description of the Prior Art
In the conventional computer graphics, there have been adopted various methods of forming stereographic curved surfaces. In one example thereof, data of plural fundamental curved surfaces (referred to as primitive curved surfaces) representative of a cylinder, a sphere, etc. are previously prepared and a new curved surface can be formed, as required, in combination with these primitive curved surfaces. In another example thereof, points on a curved surface to be newly formed are designated as control points and a curved surface passing through these control points is interpolated on the basis of a spline function.
In these prior art methods, the basic concept is as follows: the external shapes of primitive curved surfaces are previously determined as fundamental shapes and a required curved surface is formed by deformation-processing the curved surfaces on the basis of the above fundamental shapes. Therefore, it is possible to form a satisfactory curved surface, in practical use, as long as the external appearance or the shape of a mechanical object is represented.
In the case where a curved surface is formed on the basis of a spline function, in practice, since it is necessary to set a great number of control points, the control points should be determined within a practically allowable range by the use of primitive curved surfaces or by the combination of cross-sections thereof in order to form a great number of control points. Therefore, the features of this method are practically the same as in the case where primitive curved surfaces are combined with each other.
However, in the case where a curved surface representative of a human face, for instance, should naturally be formed so as to provide a soft facial expression (referred to as a free curved surface) different from the primitive curved surfaces, it is not practically satisfactory to adopt the prior art methods of forming a curved surface, because the features of the primitive curved surfaces exert a strong influence upon the formed curved surface.
In addition, in forming a new curved surface, it is impossible to readily obtain a curved surface appropriately agreeing with the one which the operator wants to obtain, unless the correlation between an image represented on the display screen on the basis of the image data to be processed by a computer and data to be controlled or determined by the operator is easy to understand intuitively. Therefore, it is preferable that parameters inputted by the operator and the resultant change in the curved surface on the display screen should have an intuitive mutual relationship for providing a better operation.